Lattice low-density parity check codes and their application in partial response systems

This paper introduces a combinatorial construction of high rate low-density parity check codes based on two-dimensional integer lattices. A class of codes with a wide range of lengths, column weights and minimum distances is obtained. The resulting codes are doubly circulant, i.e. the matrix of parity checks is an array of circulant matrices. The bounds on the minimum distance are established and the performance of these codes in partial response channels is investigated.